# Questions tagged [complex-networks]

The complex-networks tag has no usage guidance.

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### What are the right mathematical tools / language to analyse complex networks over time?

In this article about human physiology as a complex network the authors say that:
"Lacking adequate analytic tools and a theoretical framework to probe
interactions within and among diverse ...

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### Derivation of a series expansion

I am trying to derive the critical coupling strength for synchronisation in a network of phase oscillators with noisy input.
I am following the steps outlined in
Sakaguchi, Hidetsugu. "...

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### Is a function of a centrality measure a centrality measure?

I have been trying to wrap my head around the following question. Suppose you a have a centrality measure for a weighted, undirected network. Let's call the calculated centralities with $\pmb{x}>0$....

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### Which infinite random graphs with percolation threshold $p_c=0$ are transient?

I am interested in long-range percolation models with heavy-tailed degree distributions such as DHH13, GLM21, Y6. The simplest example is scale-free percolation in which vertices are elements $\mathbb{...

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### Weighted network centrality measure

I am looking for some references (I could not find much online) and/or technical guidance on the eigenvector centrality. More specifically on its generalization for a weighted network, i.e. how to ...

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### what is the computational complexity of Louvain algorithm?

I am not able to find out the computational complexity of the Louvain Algorithm. Can anyone here help me? link of the paper given below:
DOI: 10.1088/1742-5468/2008/10/P10008
https://doi.org/10.1038/...

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### Random subgraph properties

Consider a graph $G$ of $N$ vertices and $M$ edges, and assume $G$ has typical complex network properties: it is not necessarily connected, but it has a high clustering coefficient and a giant ...

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### How much algebra is preferable for studying/doing research in dynamical/complex system and networks

I asked this question earlier on Mathematics StackExchange (link), but I think it might be better to put it here.
This question seems quite broad to ask...
The situation here is that I'm a second-...

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### The topological complexity of polytopes

Polytopes arise naturally when modelling fundamental structures in Biology such as RNA and proteins [1,2]. Recently, it occurred to me that a complexity measure on the topology of polytopes might be ...

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### Research-level blogs on complex networks:

I'm an applied mathematician that has a research interest in complex networks for modelling biological systems and I wondered whether the MathOverflow community might know of research-level blogs that ...

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### Adjacency definition for a directed graph

For an undirected graph, we know that nodes are adjacent to each other if there is a link that connects them. What about adjacency for directed graphs? Is it based on:
outgoing links: node $n$ is ...